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# of n for which 50^n<7^p<50^(p+1) forms a sequence

Source: France 1994 P1

May 7, 2021
Sequencealgebra

Problem Statement

For each positive integer nn, let InI_n denote the number of integers pp for which 50n<7p<50n+150^n<7^p<50^{n+1}.
(a) Prove that, for each nn, InI_n is either 22 or 33. (b) Prove that In=3I_n=3 for infinitely many n∈Nn\in\mathbb N, and find at least one such nn.
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